CN103321621A - Heavy oil displacement method using wedged vicious slug - Google Patents

Abstract

The invention relates to a heavy oil displacement method using a wedged vicious slug. The method includes the steps of 1, dividing a nonhomogeneous reservoir into a plurality of layers according to water absorbing capacities, and acquiring permeability Ki of each reservoir; 2, designing three slugs, namely a pre-slug, a main wedged slug and a trailed slug, according to the permeabilities Ki and the physical properties in heavy oil and reservoirs; 3, alternately injecting the heavy oil reservoir with the pre-slug which is prepared with low-concentration B III-type poly-surfactant and which enters a high permeability layer to emulsify crude oil; 4, injecting the reservoirs with the main wedged slug for multiple rounds; and 5, injecting the trailed slug with low-concentration B III-type poly-surfactant or fresh water generally. In each round, the main wedged slug is divided into three small slugs; the small slugs in each round are combined by regulating the corresponding concentrations by the B III-type poly-surfactant according to formation permeability. According to the method, the nonhomogeneous heavy oil reservoirs are emulsified to reduce viscosity, the wedged equivalent vicious slug is used for equi-fluidity displacement, and swept volume is increased; accordingly, recovery efficiency of heavy oil can be further increased, investment can be reduced and operation can be simplified.

Description

Viscous crude wedge shape viscosity slug flooding method

Technical field:

The present invention relates to the flooding method of a kind of heterogeneous body viscous crude oil reservoir in the field of petroleum exploitation, especially a kind of viscous crude wedge shape viscosity slug flooding method.

Background technology:

Along with the continuous exploitation of oil, in the world petroleum reserves especially high-quality, easily the oilreserves of quarrying constantly reduces, in explored petroleum resources, the viscous crude proportion is increasing.China has abundant viscous crude resource, in the Liaohe River, oil field such as Kelamayi, Xinjiang, triumph and Henan, North China, grand celebration is distributed with heavy crude reservoir.

Viscous crude because of its viscosity height, be difficult to exploit with conventional method.Because the viscosity of viscous crude is very responsive to temperature, so the main method of heavy crude producing is thermal recovery processes at present, as steam soak and steam flooding.Steam soak and steam flooding be at present common, use thickened oil recovery technology widely.They are the viscosity-temperature dependencies of utilizing viscous crude special, in oil reservoir, inject vapours, the viscosity of crude oil is reduced greatly, thereby improved the fluid ability of crude oil, play the effect of heavy crude producing and volume increase, the mechanism of steam soak and steam flooding comprises that mainly viscous crude cracking under reduction viscosity of crude, high temperature de-plugging, the expansion that reduces interfacial tension, fluid rock and the high temperature, viscosity reduce.Though steam soak, steam flooding have been a comparatively mature technique, still have certain limitation.In cyclic steam stimulation viscous crude method, handle up can only the extraction well wellbore near crude oil in the stratum, and still have a large amount of viscous crude to fail extraction between well, its recovery ratio only is 10%～20%, carry out steam driving exploitation behind the steam soak, can make the crude oil extraction ground in a part of well formation, can further improve the recovery ratio 20%～30% of viscous crude, but the heat energy of this method consumption is many, the investment is big, technical sophistication, have a big risk, and the output of steam flooding is littler than the output of steam soak at present.

Recovery ratio, minimizing investment in order further to improve viscous crude simplify the operation, and have therefore proposed to utilize chemical agent to cooperate the theory of new flooding method displacement viscous crude.

Summary of the invention:

The invention reside in and overcome the problem that exists in the background technology, and a kind of viscous crude wedge shape viscosity slug flooding method is provided.This viscous crude wedge shape viscosity slug flooding method by heterogeneous body viscous crude oil reservoir reducing viscosity by emulsifying, with the flooding method of mobility displacements such as wedge shape equivalent viscosity slug implementation, increase swept volume, can further improve recovery ratio, the minimizing investment of viscous crude, simplifies the operation.

The present invention solves its problem and can reach by following technical solution: this viscous crude wedge shape viscosity slug flooding method may further comprise the steps:

Step 1: according to the water absorbing capacity size, non-homogeneous pay is divided into some layers, obtains each layer permeability K _i

Step 2: according to permeability K _iSize, viscous crude and reservoir properties characteristics design three part slugs, are respectively preposition slug, main body wedge shape slug and slug in hot pursuit;

Step 3: take over the preposition slug of injection to thick oil reservoir; Described preposition slug is made into by the poly-table of the B III type agent of low concentration, enters high permeability formation, the effect of performance emulsified crude oil;

Step 4: inject many rounds main body wedge shape slug to reservoir, each round main body wedge shape slug is divided into 3 pills, and the pill in each round is to be made up according to stratum permeability characteristics regulation and control respective concentration by the agent of the poly-table of B III type; Main body wedge shape slug is to be made of many round branch wedge shapes, every round is wedge shape multistage plug from high to low by viscosity and forms, main body slug viscosity profile order be first, second and third etc. the round equivalent viscosity raise gradually, divide interior first, second and third viscosity such as slug such as grade of wedge wheel to reduce gradually, reach the overall viscosity requirement of satisfying each slug by adjusting the poly-table of B III type agent concentration size, according to stratum non-homogeneity difference, the fluid that injects preferentially enters the high stratum of permeability, therefore in each wedge, the fluid components that leading portion viscosity is big enters high permeability zone; The medium-viscosity slug injects behind the high viscosity slug, and the high permeability formation position is occupied by the viscous pill fluid, has to enter middle permeable formation; The low viscosity slug injects behind the medium viscosity slug, high, in ooze the position by high, in sticking slug fluid occupy respectively, low viscosity fluid can only enter less permeable layer.A plurality of wedge actings in conjunction have formed the whole driving of the high, medium and low oil seepage layer of oil reservoir and mobility, flow velocity have all been equated, have reduced the displacement fluid and have wasted along the high permeability zone channelling;

Step 5: slug in hot pursuit generally injects the poly-table agent of B III type or the clear water of low concentration.

The poly-table of the special-purpose injecting B III type that adopts agent performance characteristics:

1, the emulsification of crude oil viscosity reducing effect is good, amplitude is big

Water: during oil (50%:50%), begin emulsification during injecting content 0.03%, emulsifiability was stable in 0.04%～0.1% o'clock; Ground degassing viscous crude, injecting viscosity reduction amplitude is big, and viscosity of crude is dropped to below the 200mPa ﹒ s by 2100mPa ﹒ s, can realize that reducing viscosity by emulsifying is more than 90%.

2, chemical injecting consumption is few

The injecting of adding 0.03%～0.08% satisfies field requirement, and it is big that a ton chemical agent consumption increases oily amplitude, and it is obvious to improve the recovery ratio effect, and indoor heterogeneous core simulated experiment and numerical simulation study can improve 15 percentage points of recovery ratios.

3, be convenient to etc. the enforcement of mobility scheme

Main by adjusting the concentration of injecting, satisfy in field conduct preceding technology and the technological requirement of each slug in the round of back easily.

4, water-soluble, can annotating performance, to control water well effective

Good water solubility is scurried into formation water and is dissolved in the viscosity injecting, reduces the mobile channelling that reduces, and chemical agent can inject with the conventional plunger pump after disperseing slaking, does not have specific (special) requirements, and injection pressure is appreciated suitably.

5, compatibility is good

It is anti-swollen to add cheap expansion-resisting agent realization in preposition slug, injects with the polymer slug combination, does not influence and improves the recovery ratio effect.

The present invention compares with the above-mentioned background technology can have following beneficial effect: this viscous crude wedge shape viscosity slug flooding method, wedge shape equivalent viscosity slug is made of preposition section, many rounds wedge shape main body multistage plug and slug in hot pursuit, according to viscous crude and the design of reservoir properties characteristics, take over to thick oil reservoir successively and inject preposition slug, many rounds main body wedge shape slug and slug in hot pursuit, utilization has emulsified crude oil, reduces the poly-table of the B III type agent displacement of viscosity of crude, forms wedge shape jointly at preposition slug, main body slug, slug in hot pursuit and involves under the effect mobility displacements such as whole realization.The agent of the poly-table of B III type possesses thick-oil emulsified adhesive-reducing increase flowability, the reduction surface tension improves characteristics such as oil displacement efficiency and higher equivalent viscosity control mobility, and can adjust its concentration according to crude oil and reservoir properties distribution characteristics and satisfy the viscosity requirement.Improve recovery ratio, rate of oil production, the basic principle that reduces injecting and system capacity is the systemic effect that physics chemical action combines, under mechanical function, make the chemical agent that possesses these characteristics can farthest contact viscous crude, involve viscous crude in the wedge shape mode and enlarge swept volume gradually, mobilities such as final realization improve overall swept volume; Making and be touched thick-oil emulsified adhesive-reducing, reduce surface tension increases mobile and the raising oil displacement efficiency, the overall realization improved swept volume, oil displacement efficiency and reduced system's displacement pressure gradually, increase substantially recovery ratio and save chemical injecting, system capacity, reach the purpose that improves overall exploitation benefit.

Description of drawings:

Accompanying drawing 1B III type poly-table agent concentration and viscosity relationship curve;

Accompanying drawing 2 is layer model anisotropically;

Accompanying drawing 3 each slug inject the stratum and advance the situation schematic diagram;

Accompanying drawing 4 each slug viscosity wedge shape distribution map;

Accompanying drawing 5 each slug swept volume design sketch.

The specific embodiment:

Below in conjunction with accompanying drawing will the invention will be further described:

Embodiment 1

Heterogeneous body viscous crude oil reservoir wedge shape viscosity slug flooding method,

Step 1: according to the water absorbing capacity size, non-homogeneous pay is divided into some layers, obtains each layer permeability K _i

Step 2: according to permeability K _iSize, viscous crude and reservoir properties characteristics design three part slugs, are respectively preposition slug, main body wedge shape slug and slug in hot pursuit;

Step 3: take over the preposition slug of injection to thick oil reservoir; Described preposition slug is made into by the poly-table of the B III type agent of low concentration, and the poly-table of B III type agent concentration is 500mg/L, enters high permeability formation, the effect of performance emulsified crude oil; In preposition slug, also can inject one section water earlier, open up low-yield water channel.

Step 4: inject many rounds main body wedge shape slug to reservoir.Each round main body wedge shape slug is divided into 3 pills, and the pill in each round is to be made up according to stratum permeability characteristics regulation and control respective concentration by the agent of the poly-table of B III type.Main body wedge shape slug is to be made of many round branch wedge shapes, and every round is wedge shape multistage plug from high to low by viscosity and forms.Main body slug viscosity profile order be first, second and third etc. the round equivalent viscosity raise gradually, divide that first, second and third viscosity such as slug such as grade reduces gradually in the wedge wheel.Reach the overall viscosity requirement of satisfying each slug by adjusting the poly-table of B III type agent concentration size.According to stratum non-homogeneity difference, the fluid of injection preferentially enters the high stratum of permeability, and therefore in each wedge, the fluid components that leading portion viscosity is big enters high permeability zone; The medium-viscosity slug injects behind the high viscosity slug, and the high permeability formation position is occupied by the viscous pill fluid, has to enter middle permeable formation; The low viscosity slug injects behind the medium viscosity slug, high, in ooze the position by high, in sticking slug fluid occupy respectively, low viscosity fluid can only enter less permeable layer.A plurality of wedge actings in conjunction have formed the whole driving of the high, medium and low oil seepage layer of oil reservoir and mobility, flow velocity have all been equated, have reduced the displacement fluid and have wasted along the high permeability zone channelling.

Described main body wedge shape slug is made up of the poly-table of the different viscosities B III type agent of a plurality of rounds, according to oil reservoir heterogeneous body situation, select then the variable concentrations fluid to make up the displacement slug according to corresponding viscosity difference and be injected into oil reservoir, automatically shunt according to fluid self fluid ability difference, formation to the oil reservoir height, in low oil reservoir is whole drives, reduce the displacement fluid significantly and waste along the high permeability zone channelling.

The definite available following formulae express of described viscosity:

$\frac{k_g}{{\mathrm{\μ}}_g}=\frac{k_z}{{\mathrm{\μ}}_z}=\frac{k_d}{{\mathrm{\μ}}_d}---\left(1\right)$

Wherein, k _g, k _z, k _dBe respectively high, medium and low permeable formation permeability, μ _g, μ _z, μ _dBe the combined slug viscosity of successively injecting.

Poly-table agent concentration and viscosity corresponding relation are seen Fig. 1.

Step 4: section in hot pursuit is injected the poly-table agent of B III type or the clear water of low concentration, and the poly-table of described B III type agent concentration is 500mg/L.

Stratum non-homogeneity situation is seen Fig. 2, because oil reservoir longtitudinal dispersion rate skewness one, the longtitudinal dispersion rate there are differences, for guaranteeing that the oil in each oil reservoir can be by effectively displacement, need to utilize by the poly-table of the B III type agent of variable concentrations and the mobility displacement such as finish, by designing many rounds wedge shape slug (slug viscosity), realize the high strength displacement of each oil reservoir.Oil displacement process is seen Fig. 3.

Among the present invention, preposition slug is to inject the agent of poly-table by leading portion injection water and back segment to constitute, the water that injects and the agent of poly-table all enter high permeability formation and flow, opened up low-yield water channel, utilize the emulsification of poly-table agent can further be emulsified in the crude oil that many rounds main body wedge shape slug displacement of reservoir oil of injecting thereafter is pushed through preposition slug afterbody in addition, this part crude oil is because when inferior main body wedge shape slug effect stratum, Duolun, crude oil in the different permeable formations is by in the displacement process, in some, the part crude oil that less permeable layer is displaced can flow soon (surpassing the high viscosity slug), and then flows in the high permeability formation of high viscosity slug front.Preposition slug displacement of reservoir oil function has been mainly reflected in increase in-place oil flowability, reduces crushing, saves mobility principal pieces such as system capacity focuses on beyond the Great Wall.Main body wedge shape slug is to be made of many round branch wedge slugs, and the branch wedge slug of each round is made of three pills usually, and the viscosity magnitude relationship of three pills is that to require successively according to the sequencing that injects be high, medium and low relation.In main body slug injection process, successively the branch wedge slug equivalent viscosity of the first, second, third, etc. round of injecting successively improves gradually, overall displacement process constantly utilizes poly-table agent emulsification in-place oil, enlarge swept volume gradually, final realization waits the mobility cumulative to improve swept volume to greatest extent.In the branch wedge slug of each round, first pill of Zhu Ruing (viscosity height) can preferentially enter high permeability formation in advance, second pill (viscosity is medium) enters the stratum subsequently, high permeability formation is by the first segment filling, has only other low relatively interval of the permeability of flowing to, the 3rd pill (viscosity is low) in like manner can only enter the lower permeable formation of permeability, the slug by different viscosities made up realize different permeabilities stratum wait the mobility displacement.Reservoir swept volume shape is progressively expanded with the wedge shape state, branchs wedge slug is reverse with the wedge shape tapering that the swept volume expansion presents according to the wedge shape tapering that the viscosity size presents in each round, and whole preposition slug, the combination of main body slug are expanded in the same way according to wedge shape and swept volume that the viscosity variation presents.Fig. 4 is seen in slug feature and round injection in proper order, and each slug improves the swept volume effect and sees Fig. 5.Water-sensitive formation should be taked the anti-anaphylaxis technical measures, and each slug is formulated by the poly-table of the B III type agent of variable concentrations, and under special-purpose injecting and the acting in conjunction of wedge shape flooding method, viscosity of crude is reduced and has increased substantially swept volume and oil displacement efficiency; Inject slug in hot pursuit at last as the supporting slug that waits the mobility displacement of reservoir oil, the performance of accessory system general effect.

In oil displacement process, the order that each slug injects is to inject slug 1,2 earlier, finish preposition slug effect, because stratum heterogeneous body, each layer permeability contrast, outside fluid enters the stratum can preferentially enter the low high permeability formation of filtrational resistance, so slug 1 and 2 enters high permeability formation, brings into play preposition slug effect.Main body wedge shape slug is the branch wedge slug that has been made of 3 rounds combined slug 3,4,5, combined slug 3 is to be made of three pills, be respectively slug 3-1,3-2,3-3, after finishing preposition slug injection, slug 3-1 enters the stratum, preferentially enter high permeability formation, slug 3-2 injects subsequently, according to fluid flow characteristics, can preferentially enter high permeability formation, but this moment high permeability formation by full-bodied slug 3-1 filling, so slug 3-2 is just mobile to other permeable formation, then slug 3-3 enters the stratum subsequently, in like manner can only flow to other low-permeability layer.In like manner, the combined slug 4 of amiable injection and 5 also is that 3 pills have occupied different permeable formations respectively.Under preposition slug (slug 1,2) and main body slug (slug combination 3,4,5) acting in conjunction, what the slug viscosity of formation presented is wedge shape, and the swept volume on stratum has equally also been formed wedge shape, has effectively enlarged swept volume, has improved oil recovery factor.

Slug 1 and 2 constitutes preposition slug together, and wherein slug 1 is water, and slug 2 is low viscous injecting, and the effect of water channel, emulsified crude oil reduction viscosity is opened in performance.

Slug 3-1,3-2,3-3 constitute the first round wedge in the principal piece plug, wherein viscosity relationship μ _3-1μ _3-2μ _3-3, slug 4-1,4-2,4-3 constitute second in the principal piece plug and take turns wedge, wherein viscosity relationship μ _4-1μ _4-2μ _4-3, slug 5-1,5-2,5-3 constitute the third round wedge in the principal piece plug, wherein viscosity relationship μ _5-1μ _5-2μ _5-3In the principal piece plug oil displacement process, μ in first round _3-1Viscosity is the highest, and greater than in-place oil viscosity, the high viscosity slug preferentially enters high permeability formation K after entering the stratum ₁, after inferior viscosity slug enters, because viscosity is low, on the high section of oozing is stifled by the first viscosity section, have only the low relatively infiltration section of the flow direction, the 3rd viscosity section in like manner enters low infiltration section again, realizes that high permeability formation involves to the expansion of low-permeability layer.In addition, analyze the speed with three slugs in the round, according to Darcy's law, slug at the stratum medium velocity is:

$v=\frac{k}{\mathrm{\μ}}\·\frac{\mathrm{\Δp}}{\mathrm{\ΔL}}$

According to the minimal flow resistance principle, the high viscosity slug of injection at first enters high permeability formation, with v ₁Speed move forward.

$v_1=\frac{k_1}{{\mathrm{\μ}}_{3-1}}\·\frac{\mathrm{\Δp}}{\mathrm{\ΔL}}$

The medium viscosity slug that injects in the speed of high permeability formation is:

$v_2=\frac{K_1}{{\mathrm{\μ}}_{3-2}}\frac{\mathrm{\Δp}}{\mathrm{\ΔL}}$

Because μ _3-1μ _3-2So, v ₁＜v ₂Under the effect of front and back pressure reduction, the medium viscosity slug will turn to permeability formation in the inflow, with v ₂' speed move forward, namely

${{\mathrm{<figure-callout\; id="2"\; label="v"\; filenames="HDA00003394330800022.png"\; state="\{\{state\}\}">v</figure-callout>}}_2}^{\&prime;}=\frac{{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HDA00003394330800022.png"\; state="\{\{state\}\}">k</figure-callout>}}_2}{{\mathrm{\&mu;}}_{3-2}}\&CenterDot;\frac{\mathrm{\&Delta;p}}{\mathrm{\&Delta;L}}$

The speed v of follow-up little viscosity slug in height infiltration, middle permeable formation ₃, v ₃' be respectively:

${\mathrm{<figure-callout\; id="3"\; label="v"\; filenames="HDA00003394330800012.png"\; state="\{\{state\}\}">v</figure-callout>}}_3=\frac{k_1}{{\mathrm{\&mu;}}_{3-1}}\&CenterDot;\frac{\mathrm{\&Delta;p}}{\mathrm{\&Delta;L}},$ ${{\mathrm{<figure-callout\; id="3"\; label="v"\; filenames="HDA00003394330800012.png"\; state="\{\{state\}\}">v</figure-callout>}}_3}^{\&prime;}=\frac{{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HDA00003394330800022.png"\; state="\{\{state\}\}">k</figure-callout>}}_2}{{\mathrm{\&mu;}}_{3-3}}\&CenterDot;\frac{\mathrm{\&Delta;p}}{\mathrm{\&Delta;L}}$

In like manner, because μ _3-1μ _3-2μ _{3-3 is little}, k ₁K ₂K ₃, then have:

v ₃>v ₂>v ₁，v ₃'>v ₂'

Under the effect of front and back pressure reduction, little viscosity slug enters low permeability formation, with speed v ₃" move forward.

${{\mathrm{<figure-callout\; id="3"\; label="v"\; filenames="HDA00003394330800012.png"\; state="\{\{state\}\}">v</figure-callout>}}_3}^{\&prime;\&prime;}=\frac{{\mathrm{<figure-callout\; id="3"\; label="k"\; filenames="HDA00003394330800012.png"\; state="\{\{state\}\}">k</figure-callout>}}_3}{{\mathrm{\&mu;}}_{3-3}}\&CenterDot;\frac{\mathrm{\&Delta;p}}{\mathrm{\&Delta;L}}$

Work as v ₁=v ₂'=v ₃" time, the multistage plug advanced in unison in the high, medium and low permeable formation.

By that analogy, when the second round wedge shape slug is combined into the stratum, realized that also high permeability formation involves to the expansion of low-permeability layer.

The agent of the poly-table of the B III type that adopts is available from Shanghai Hai Bo company.

Claims (6)

1. viscous crude wedge shape viscosity slug flooding method may further comprise the steps:

Step 1: according to the water absorbing capacity size, non-homogeneous pay is divided into some layers, obtains each layer permeability K _i

Step 2: according to permeability K _iSize, viscous crude and reservoir properties characteristics design three part slugs, are respectively preposition slug, main body wedge shape slug and slug in hot pursuit;

Step 3: take over the preposition slug of injection to thick oil reservoir; Described preposition slug is made into by the poly-table of the B III type agent of low concentration, enters high permeability formation, the effect of performance emulsified crude oil;

Step 4: inject many rounds main body wedge shape slug to reservoir, each round main body wedge shape slug is divided into 3 pills, and the pill in each round is to be made up according to stratum permeability characteristics regulation and control respective concentration by the agent of the poly-table of B III type; Main body wedge shape slug is to be made of many round branch wedge shapes, every round is wedge shape multistage plug from high to low by viscosity and forms, main body slug viscosity profile order be first, second and third etc. the round equivalent viscosity raise gradually, divide interior first, second and third viscosity such as slug such as grade of wedge wheel to reduce gradually, reach the overall viscosity requirement of satisfying each slug by adjusting the poly-table of B III type agent concentration size, according to stratum non-homogeneity difference, the fluid that injects preferentially enters the high stratum of permeability, therefore in each wedge, the fluid components that leading portion viscosity is big enters high permeability zone; The medium-viscosity slug injects behind the high viscosity slug, and the high permeability formation position is occupied by the viscous pill fluid, has to enter middle permeable formation; The low viscosity slug injects behind the medium viscosity slug, high, in ooze the position by high, in sticking slug fluid occupy respectively, low viscosity fluid can only enter less permeable layer.A plurality of wedge actings in conjunction have formed the whole driving of the high, medium and low oil seepage layer of oil reservoir and mobility, flow velocity have all been equated, have reduced the displacement fluid and have wasted along the high permeability zone channelling;

Step 5: slug in hot pursuit generally injects the poly-table agent of B III type or the clear water of low concentration.

2. viscous crude wedge shape viscosity slug flooding method according to claim 1 is characterized in that: inject one section water in the described step 3 in the preposition slug earlier.

3. viscous crude wedge shape viscosity slug flooding method according to claim 1 is characterized in that: the poly-table of described preposition slug B III type agent concentration is 500mg/L.

4. viscous crude wedge shape viscosity slug flooding method according to claim 1 is characterized in that: the poly-table of described slug B III type in hot pursuit agent concentration is 500mg/L.

5. viscous crude wedge shape viscosity slug flooding method according to claim 1, it is characterized in that: described main body wedge shape slug is made up of the poly-table of the different viscosities B III type agent of a plurality of rounds, according to oil reservoir heterogeneous body situation, select then the variable concentrations fluid to make up the displacement slug according to corresponding viscosity difference and be injected into oil reservoir, automatically shunt according to fluid self fluid ability difference, form to the oil reservoir height, in low oil reservoir is whole drives.

6. viscous crude wedge shape viscosity slug flooding method according to claim 5 is characterized in that: formulae express below described viscosity definite available:

$\frac{k_g}{{\mathrm{\&mu;}}_g}=\frac{k_z}{{\mathrm{\&mu;}}_z}=\frac{k_d}{{\mathrm{\&mu;}}_d}---\left(1\right)$

Wherein, k _g, k _z, k _dBe respectively high, medium and low permeable formation permeability, μ _g, μ _z, μ _dBe the combined slug viscosity of successively injecting.

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